High Tc superconducting magnetic bearings are generally, but not essentially, constructed with a superconducting stator element which is maintained at a temperature below or about 77K with liquid nitrogen and a levitated permanent magnet rotor element. The bearing load is determined by the critical current density which in turn depends upon the motion of magnetic flux lines. At about 77K the flux lines within a high Tc superconducting material can be pinned strongly to fixed positions, and recent advances in pinning technology have been successful in raising the load capacity of superconducting bearings considerably. Vibration of the bearing causes vibrational movement of the rotor relative to the stator. The magnetic field of the permanent magnet rotor is highly inhomogeneous and consequently the vibration creates an AC field in the superconductor. This AC field can cause the flux lines in the stator to depin and move. Moving flux lines dissipate energy and hence the load capacity of the bearing is reduced. However, as the load capacity increases the capacity for damping is reduced considerably, especially at low vibrational amplitudes. The dissipation of energy in high Tc superconductors induced by an AC magnetic field is the result of the movement (depinning) of the flux lines. It is known (J. Supercond. 6 (1993) 201. E. H. Brandt) that high Tc superconductors have a non-monotonic temperature dependence of energy dissipation. At low temperatures (of the order of 50-55K) the flux lines are pinned and the AC field can only induce the motion of flux lines inside the potential well, which leads to very low energy dissipation. At this limit, flux motion occurs only at a thin surface layer. At high temperatures, of the order of 91-92K but still below Tc, the flux lines are completely mobile due to strong thermal fluctuations. In this situation flux motion occurs throughout the material; however, since the pinning is weak the flux lines are subjected to very weak drag forces resulting in low AC losses. It has been discovered, however, that between these temperature limits there is a very narrow temperature range in which the flux lines are weakly pinned but flux motion induced by the AC field reaches the center of the superconducting sample. This range corresponds to a maximum in energy dissipation by AC losses. Therefore, by controlling the temperature of a high Tc superconducting damping element within a very narrow range, it is possible to switch on or switch off a vibrational damping effect in the bearing or other magnetic levitation device.